Interpolate mesh surface between curves
I think what you want here is the Grid Fill tool. 

Make your two profiles (make sure they have the same number of vertices), then fill them in with Ctrl+F > Grid Fill. 
Make sure you have Tools menu opened (you can toggle it on and off with the T key, it shows up on the left of the 3D viewport) or press F6 after command execution and you can fiddle with the settings; I recommend you using a very low setting and then use loopcuts. 

The cuts will have the right shape, so all you have to do is push them up or down the opposite axis from your main profile shapes. (If it was a floor or roof, this would be Z, a wall would be either X or Y.)